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Session 37. Wild algebraic and geometric topology
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Cotorsion and Homology |
Wolfgang Herfort, University of Technology, Vienna, Austria
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The talk is based on the joint work with Wolfram Hojka
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The classical concept of cotorsion of an abelian group is here
characterized in the style of algebraic compactness, namely by the existence
of solutions of certain systems of equations. This approach further
highlights the close relation between the two concepts. Then the natural
extension to nonabelian groups is related to a topological property
and used to determine the first singular homology group of wild spaces.
As a further application, it is shown that the abelianization of the quotient
\(\ast_i^\sigma G_i /(\ast_i G_i )\) is isomorphic to \(\prod_i\mathbb Z/ \bigoplus_i \mathbb Z\),
for arbitrary nontrivial
groups \(G_i\) of cardinality at most the continuum.
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